Radiosity with intersecting or touching surfaces

ABSTRACT

Image data is generated for a scene, in which the scene includes object surfaces in three-dimensions. Intersecting or touching surfaces are identified by analysing the surfaces within a hierarchy of bounding volumes. Thereafter, a multi-resolution representation of a radiosity equation is constructed for the scene, wherein one of the identified surfaces is considered separately for light emission on either side of a previously identified line of contact or intersection.

This application is a Continuation of application Ser. No. 09/261,145,filed on Mar. 3, 1999 now U.S. Pat. No. 6,366,283, entitled “GENERATINGIMAGE DATA”, which application is incorporated herein by reference.”

FIELD OF THE INVENTION

The present invention relates to generating image data, wherein aplurality of surfaces are defined in three dimensional space.

BACKGROUND TO THE INVENTION

Several procedures are known for rendering images containing elementsdefined as three-dimensional data. A known approach to generating imagesof photo-realistic quality is to consider reflections between allelements simultaneously. The light emission of any given element isconsidered as being dependent upon the sum of contributions from allother elements and a set of equations is defined that represents theseinteractions. The light emission values for all the elements are thendetermined simultaneously by solving a system of equations.

This procedure is known as radiosity simulation. Surfaces of objects aresub-divided into mesh elements of varying sizes in order to determine anappropriate level of resolution required to represent the change inbrightness that will be encountered across the surface of the object.The total number of mesh elements required for a scene is typically verylarge, and the resulting system of equations is also extremely large.Several refinements to radiosity simulation have been established inorder to make implementation of this method practical for scenescontaining large numbers of objects.

A known advantage of radiosity simulation is that once the system ofequations has been solved, and light emission values determined, thelight emission of mesh elements may be considered as view independent,resulting in a separate radiosity rendering process that is capable ofrendering a view from any position. The high efficiency of radiosityrendering makes radiosity particularly suitable for demandingapplications, such as generating long sequences of image data frames forfilm or video, or generating image data in real-time.

In the process of radiosity simulation, the presence of intersectingsurfaces may result in problems being encountered when surfaces aresub-divided into mesh elements, and element boundaries do not coincidewith surface intersections. This results in inappropriate brightnessvalues being encountered at such intersections. A known method foravoiding this problem is to identify intersecting surfaces prior tosubdivision into mesh elements, and to create mesh element boundariesalong such intersections.

Radiosity simulation is increasingly used for the generation ofphoto-realistic scenes, comprising many tens of thousands of polygons,of which object surfaces are comprised. Identification of intersectingpolygons as a prior step to constructing a radiosity simulation equationis therefore restricted by the number of combinations of intersectingpolygons that must be checked. For example, if fifty thousand polygonsare present in a scene, the number of potential intersections that mustbe checked, according to known methods, would be five times ten raisedto the power of eight (5×10⁸). Checking each individual pair of polygonsfor intersection is a non-trivial mathematical operation. In practice,therefore, the identification of intersecting surfaces inphoto-realistic scenes is impossible to achieve directly, using knownmethods, and operator intervention is necessary in order to identifysurfaces where such problems occur.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention, there is provideda method of generating image data for a scene, wherein said sceneincludes object surfaces in three-dimensions, comprising the steps ofidentifying intersecting or touching surfaces by analysing said surfacewithin a hierarchy of bounding volumes; and constructing amulti-resolution representation of the radiosity equation for saidscene, wherein one of said identified surface is considered separatelyfor the light emission on either side of a line of contact orintersection.

In a preferred embodiment, the step of identifying intersecting ortouching surfaces by analysis of bounding volumes, includes thecomponent steps: considering bounding volumes and surfaces as items;identifying pairs of items; determining whether both items in the pairare surfaces; determining an overlap of items or an intersection ofsurfaces; and upon a condition of overlap, recursing the above componentsteps, retaining the smaller item and selecting another; or uponcondition of an intersection, storing an indication of this condition;or upon condition of an intersection, storing an indication of thiscondition.

Preferably, the hierarchy of bounding volumes is created for the dualpurpose of identifying intersecting or touching surfaces, and anadditional method for generating image data from said scene.

According to a second aspect of the present invention, there is providedapparatus for generating image data from scene data, includingprocessing means, and storage means for storing said scene data and forstoring instructions for said processing means, wherein said sceneincludes object surface in three-dimensions and said instructions arearranged to control said processing means to perform the steps of:identifying intersection or touching surfaces by analysing said surfaceswithin a hierarchy of bounding volumes; and constructing amulti-resolution representation of the radiosity equation for saidscene, wherein one of said identified surfaces is considered separatelyfor light emission on either side of a line of contact withintersection.

In a preferred embodiment, the apparatus is further configurable toperform the step of solving the radiosity equation. Preferably, theapparatus is further configurable to perform a step-by-step rendering ofsaid image data in response to a user specified view. Preferably, theapparatus is further configurable to include the step of rendering theimage data in response to camera data generated within a virtual set.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a system for generating image data, including a monitor anda processing system;

FIG. 2 details the processing system shown in FIG. 1;

FIG. 3 details processes performed by the processing system shown inFIG. 1 when generating image data, including a process of radiositysimulation;

FIG. 4 details an image displayed on the monitor shown in FIG. 1,including several scene objects, that include two walls and a picture;

FIG. 5A summarises light energy transfer between a pair of objects, suchas the two walls shown in FIG. 4;

FIG. 5B summarises light energy transfer between a single receivingsurface, and an arbitrary number of emitting surfaces;

FIG. 5C shows the radiosity reciprocity equation;

FIG. 5D shows the classical radiosity equation;

FIG. 6 indicates meshing strategies for the walls shown in FIG. 4;

FIG. 7 details the process of radiosity simulation, shown in FIG. 3,including processes of constructing a multi-resolution representation ofthe radiosity equation, and solving the radiosity equation;

FIG. 8 details a prior art process for constructing the multi-resolutionrepresentation of the radiosity equation shown in FIG. 7, including aprocess of executing refinement steps;

FIG. 9 details the process of executing refinement steps shown in FIG.8;

FIG. 10 illustrates data structures arising from executing therefinement process shown in FIG. 8 with respect to the objects indicatedin FIG. 4;

FIG. 11 details the process of solving the radiosity equation shown inFIG. 7, including a process of gathering the radiosity for the scene,and a process of push-pull radiosity for scene;

FIG. 12 details the solution for the process of gathering the radiosityfor the scene shown in FIG. 11;

FIG. 13 details the process of push-pull radiosity for the scene shownin FIG. 11;

FIG. 14 shows an example of a virtual scene that has been hierarchicallymeshed without taking into account the intersection of surfaces;

FIG. 15 shows the same scene as FIG. 14, but where hierarchical meshinghas taken into account the intersection of surfaces, in accordance withthe present invention;

FIG. 16 details an improved method for constructing the multi-resolutionsimulation of the radiosity equation shown in FIG. 7, including a stepof checking for intersecting polygons;

FIG. 17 details the step of checking intersecting polygons shown in FIG.16, including constructing a hierarchy of bounding volumes andrecursively checking for intersecting polygons;

FIG. 18 shows an example of a hierarchy of bounding volumes generated inaccordance with a process of constructing a hierarchy of boundingvolumes shown in FIG. 17;

FIG. 19 details the step of recursively checking for intersectingpolygons shown in FIG. 17;

FIG. 20 shows a virtual set, for generating live video data; and

FIG. 21 details equipment combining camera data with scene data inreal-time.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A system for generating image data using radiosity is illustrated inFIG. 1. The radiosity process involves performing a radiosity simulationin which light emission values are calculated for all elements in thescene, irrespective of viewing position. Thereafter, this information ismade available for particular viewing positions during radiosityrendering. The rendering process requires a sufficiently low level ofcomputation to enable image frames of high definition and high photorealism to be rendered with high efficiency.

A processing system 101, such as an Octane™ produced by Silicon GraphicsInc., supplies output image signals to a video display unit 102. A userdefines a scene in terms of objects in three dimensions, or by importingthree-dimensional scene data from a pre-existing scene structure. Theuser may also determine a stationary or moving camera position fromwhich to view the resulting rendered scene image. Rendered frames ofimage data, derived from three-dimensional scene data, are stored bymeans of a striped redundant array of inexpensive discs (RAID) 103. Thesystem receives user commands from a keyboard 104 and a graphics tablet105 operated by a pressure sensitive stylus 106.

The processing system 101 is detailed in FIG. 2. The processing systemcomprises two central processing units 201 and 202 operating inparallel. Each of these processors is a MIPS R10000 manufactured by MIPSTechnologies Incorporated, of Mountain View, Calif. A non-blockingcross-bar switch 209 permits non-blocking full bandwidth communicationbetween the two processors 201 and 202 and with a memory 203 and otherperipherals. The memory 203 includes typically two hundred and fifty-sixmegabytes of dynamic RAM. The memory is used to store instructions forthe processors, and data, including a large quantity of element datathat is required while performing the process of radiosity simulation.Input and output interface circuits are denoted as XIO in the diagramshown in FIG. 2. External connections, and connections to slowperipherals such as serial ports are made via XIO interface circuits, inorder to provide synchronisation between the peripheral circuits and theextremely high speed data paths of the main processor structure.

A first XIO interface circuit 204 provides bi-directional connections tothe RAID array 103 shown in FIG. 1. A second XIO interface circuit 205provides additional connectivity to an additional RAID array, should itbecome necessary to increase storage requirements for image data. Athird XIO interface circuit 206 provides a data connection to a network,over which three-dimensional scene data may be shared. A further XIOinterface circuit 207 facilitates connection with the stylus 105 and thekeyboard 104 shown in FIG. 1, in addition to an internal hard disk drive211, four gigabytes in size, upon which instructions for the processors201 and 202 are stored. An additional XIO interface circuit provides aconnection between the cross-bar switch 209 and a graphics processor210. The graphics processor 210 receives instructions from processors201 and 202 in such a way as to construct a two dimensional image fieldfor display on the video monitor 102.

Procedures performed by processors 201 and 202 are illustrated in FIG.3. At step 301 a user defines a three dimensional scene, which mayinvolve importing three dimensional information from an external source,for example over the network connection. At step 302 a radiositysimulation is performed, configured to analyse objects within the sceneso as to optimise their deconstruction into mesh elements, and then tocalculate a light emission value for each mesh element.

At step 303 the user defines movement of a virtual camera through thescene, defining a changing view that is known as a “walk through”. Thesame element light emission values generated by the radiosity simulationprocedure 302 may be used for any desired camera view, provided that therelative positioning of objects within the scene does not change.

At step 304 a frame is selected for rendering and at step 305 radiosityrendering is performed. In radiosity rendering, the light emission ofeach element is projected with respect to the camera position into a twodimensional image plane. At step 306 additional view-dependent renderingis added. Radiosity generates light emission values for elements,irrespective of view. This is known as view-independent rendering.However, certain aspects of a scene may require view-dependent lighting,for example, when a mirror or other highly reflective object is present.In order to achieve photo-realism, it is then necessary to combine theradiosity rendering procedure with light emission values determined by aview-dependent procedure, such as ray tracing. Given that only a smallpart of the resulting image is view dependent, the additional complexityof the ray tracing procedure need not result in an excessivecomputational increase. Alternatively, other, less realisticview-dependent procedures may be used for speed. When combined with thehigh degree of realism provided by radiosity, these can still result ina highly realistic overall image being created.

At step 307 a question is asked as to whether all of the frames for theclip have been rendered. When answered in the negative, control isreturned to step 304, whereupon the next frame of the clip is selectedand the radiosity rendering procedure 305 is repeated. Eventually, thequestion asked at step 307 will be answered in the affirmative andcontrol will be directed to step 308. At step 308 a question is asked asto whether aspects of the existing scene need to be modified in order toimprove the quality of the result. When answered in the affirmativecontrol is returned to step 301. Eventually, no further modificationswill be necessary and the question asked at step 308 will be answered inthe negative.

An example of a scene for rendering using a radiosity procedure isillustrated in FIG. 4. The scene consists of a room including a firstwall 401, a second wall 402, and a floor 403. A statue 404 equipped witha base 410 is located on the floor 403 and a picture 405 is shown hungon the wall 402. Radiosity simulation 302 is performed with reference toa light source, illustrated as light source 406, but which, because ofthe view point defined by die position of the virtual camera, does notitself appear as part of the resulting two dimensional image. Therelative positioning of the light 406 and the statue 404 results in ashadow 407 being cast on floor 403. Similarly, given the position oflight source 406, a frame 408 of picture 405 also casts a slight shadow409 against the wall 402.

The presence of a light source in the scene results in a quantity oflight energy being introduced. This light energy is scattered throughoutthe scene in a complex way, that is dependent upon the reflectivities,shapes and positioning of objects within the scene. Radiosity simulationconstructs a system of equations to represent these relationships, andis thereby able to determine light emission values that are veryrealistic.

The basic approach to performing the radiosity simulation 302 isoutlined in FIGS. 5A, 5B, 5C and 5D. FIG. 5A details two elements 501and 502 in a scene. The two elements are at right angles, such that itcan be seen that not all of the light energy from element 501 will betransferred to element 502, and vice versa. The actual proportion oflight energy transferred from one element to another is called the formfactor. If element 501 is considered to be a source element i, andelement 502 is considered to be a receiving element j, then the formfactor for the transfer of light energy per unit area from i to j isdenoted Fij. Similarly, the proportion of energy from element jtransferred to element i is denoted Fji.

It can be seen from this example that calculating the form factorrequires a determination of the visibility of the source element withrespect to the receiving element. This is made more complex if a thirdoccluding element is possibly present, which may totally or partiallyblock light transfer between the elements for which the form factor isbeing calculated. In the event that a scene comprises only two elements501 and 502, and one of these is a light source, it is possible toconstruct a pair of simultaneous equations that may be solved in orderto obtain the light emission from each element without difficulty. Inpractice, however, a scene comprises many objects, each of which mayneed to be subdivided into a mesh of elements in order to obtain asufficiently accurate representation of light variation across surfaces.

Given the form factors for all element interactions that are beingconsidered, the total brightness from an element i is obtained byconsidering the sum of light energies directed at it from all of theother elements in the scene. This relationship is illustrated in FIG.5B. The fundamentals underpinning the radiosity approach are derivedfrom notions of conservation of energy and the total light energy fluxemitted by a particular element is therefore considered as the productbetween a flux density value B and the area of the element A, identifiedas the product BA. Thus, for a particular element i, the energy fluxradiated by this element is identified as the product BiAi which is thenconsidered as equal to the self emission of the element Ei multipliedagain by its area Ai plus the sum of all light received from all of theco-operating elements. Thus, for every single co-operating element inthe scene, each instance of which is denoted by the letter j, the amountof light received by element i is equal to the flux density Bj ofelement j multiplied by the area Aj of element j multiplied by the formfactor Fji expressing the proportion of light transferred from j to i.The sum of these values is then multiplied by the reflectance Rirepresenting the reflectance of element i.

As previously stated, the procedure is underpinned by notions ofconservation of energy. Therefore, in accordance with this principle,the form factor Fij for the transfer of light energy from i to j,multiplied by the area Ai of element i is equal to the form factor Fjirepresenting the transfer of light energy from j to i multiplied by thearea Aj of j, as shown in FIG. 5C. This is known as the radiosityreciprocity equation. This relationship may be substituted into theequation of FIG. 5B to give the equation shown in FIG. 5D, which isknown as the classical radiosity equation. In FIG. 5D, the flux densityBi of element i is given by the source flux density Ei of element i plusthe reflectance Ri multiplied by the sum for each element j, of fluxdensity Bj multiplied by the form factor Fij.

The equation shown in FIG. 5D is the one used to determine lightemission values for elements in a scene. In a scene containing fiftythousand elements, the right side of this equation would have to beevaluated fifty thousand times in order to obtain an initialillumination value for a single element i. Thus, in order to calculatean initial illumination value for all fifty thousand elements, the rightside of this equation must be evaluated fifty thousand times, fiftythousand times. Furthermore, this large number is also the number ofform factors that need to be calculated before the system of equationscan be solved. Thus a radiosity simulation utilising this approach isimpractical for realistic image synthesis of scenes containing largenumbers of elements.

A solution in which a relatively low number of elements are present isillustrated at 601 in FIG. 6. The image consists of two walls, in whichthe first wall has been subdivided into four mesh elements 602 and asecond wall has also been subdivided into four mesh elements 603. Thetotal number of elements present is relatively small, thereby reducingcomputational time when evaluating the equation in FIG. 5D, but this inturn results in a coarse image having visible artefacts. This problemmay be understood by considering that, although illumination throughoutthe scene is non-linear, the illumination gradient where the walls meetchanges faster than in the middle of a wall. Thus, by rendering thescene at the level of resolution shown at 601, the shading close to theintersection of the walls will be unrealistic.

A solution to this problem is shown at 604. In this example, the wallsare the same as those identified at 601 but each wall has been dividedinto substantially more mesh elements. Thus, a first wall is made up ofsixty-four elements 605 with a similar sixty-four element mesh 606 beingpresent in the second wall. This results in a significant improvement ofthe overall realism of the image but a major increase in terms ofcomputational overhead. It can be seen that the complexity of solvingthe equation in FIG. 5D increases in proportion to the square of thenumber of elements present, when this approach is used. Furthermore, itmay be understood that while the level of meshing has been increasedwhere this is important, close to the intersection of the walls, it hasalso been increased unnecessarily in other areas.

Computational time may be reduced while maintaining image quality bytaking a hierarchical approach as illustrated at 607. In this example,the walls have been divided into a large number of small elements, suchas element 608, at positions where the interaction between the walls isgreatest. Similarly, at a distance displaced from the intersection, theelements, such as element 609, are significantly larger. In this way,good image quality is obtained while computational overhead is reduced.This type of meshing is further enhanced by only evaluating form factorsbetween mesh elements at an appropriate level of resolution. Forexample, a large mesh element at the edge of a wall need not evaluatemultiple form factors for interactions between all the small meshelements on the wall opposite that are close to the intersection.Instead, an appropriate coarse superset of the smallest mesh elements isselected for this interaction. Thus it becomes possible to consider themesh as a nested hierarchy, such that, whenever possible, coarser meshelements are used to define light exchanges. The subdivisions of coarsemesh elements are used when the predicted accuracy of light interchangeis not sufficiently high. This technique is known as hierarchicalradiosity. A data structure representing the nested levels of meshelements is known as a multi-resolution representation of the radiosityequation.

Hierarchical radiosity may still be time consuming, as there may be manythousands of objects within a scene. Thus, regardless of the efficiencyof the hierarchical mesh, there are still a minimum number ofinteractions that are defined to be the square of the number of objects.In typical photo-realistic scenes, this number may still beprohibitively high. In order to reduce the computation still further,additional procedures have been established in order to extendhierarchical radiosity. In radiosity with clustering, certaincombinations of objects, such as the statue 404 shown in FIG. 4, and itsbase 410, are considered as forming a single cluster element.Interactions with distant elements, such as those comprising a wall 402,may then be expressed by the use of a single form factor, because thelight reaching the wall from the statue is weak. The difference betweenthe statue as it is, and the statue represented, for example, as asingle radiating cylinder, will be below the required accuracy thresholdwhen calculating the form factor for transfer from the statue to thewall. Closer surfaces, such as wall 401, may need to consider the statueas comprising a number of elements, each having different light emissionvalues, in order to determine local light emission gradients withsufficient accuracy. The combination of hierarchical radiosity withclustering reduces the number of element relationships from n squared toapproximately n log n, where n is the number of mesh elements in thescene. It is this reduction in complexity that has enabled the radiositytechnique to be considered for use in many applications.

Procedure 302 for performing radiosity simulation is detailed in FIG. 7.At step 701 the multi-resolution representation of the radiosityequation is constructed. At step 702 the radiosity equation is solved.

A known procedure for the construction of a multi-resolutionrepresentation of the radiosity equation, as indicated at step 701, isdetailed in FIG. 8. At step 801 all of the scene is analysed such that ahierarchy of cluster elements is generated. At the top of this hierarchyis a cluster that represents the whole scene. Below this cluster areclusters that represent distinct groups of objects, related by theirphysical proximity. A method for hierarchical clustering of objects isdescribed in “A Clustering Algorithm for Radiosity in ComplexEnvironments”, by Brian Smits, James Arvo and Donald Greenberg,Proceedings of SIGGRAPH '94, pp.435-442, 1994. The lowest level of thecluster hierarchy is the object level. Objects themselves may beconsidered as elements, in the same way as clusters, and the meshelements which are created at a later stage of processing.

At step 802, the whole scene cluster at the top of the hierarchy ofclusters, is selected as being both a source element and a receivingelement. Thus, it is considered as transferring light onto itself. Thisapparently unlikely starting point is never in actual fact considered asa genuine light path. However, it serves to initiate the recursiverefinement process of step 803. At step 803, the whole scene isconsidered initially as emitting light to itself. The recursiverefinement process considers this as resulting in an excessively badquality of light shading, and so recursively considers the componentclusters and objects for light interactions. Furthermore, the recursiverefinement process at step 803 creates mesh elements for the surfaces ofobjects wherever this is necessary in order to represent the lightshading to a sufficient level of accuracy.

A recursive refinement process 803 shown in FIG. 8 is detailed in FIG.9. A source element and a receiving element will have been selected byeither process 802, or subsequent steps 906 or 909 within the sameflowchart. These are now initially denoted as source element i andreceiving element j at step 901. At step 902 an error is determined forthe transfer of light from i to j, wherein i and j are uniformlyemissive. Upon initial execution of the flowchart of FIG. 9, asindicated at step 803, the source element i and the receiving element jare both the same, and are the cluster element that represents the wholescene. Inevitably, the error determined for using this light path as thesole radiosity transaction for shading the entire scene results in avery large error in the quality of surface shading. Thus, on the firstexecution of the process shown in FIG. 9, as represented at step 803,the predicted error generated at step 902 will be very high.

At step 903 a question is asked as to whether a subdivision into furtherelements is required in order to improve the quality of the simulation.If the estimated error, calculated at step 902, is considered to besufficiently small, subdivision is not required and the question askedat step 903 is answered in the negative. The question asked at step 903is also answered in the negative if, within the constraints of thesystem, it is no longer possible to facilitate subdivision into smallerelements. Alternatively, if the error value estimated at step 902 is toohigh, the question asked at step 903 is answered in the affirmative.

At step 904 a question is asked as to whether it is appropriate tosubdivide the source element i or to subdivide the receiving element j.Again, an error estimation approach is taken and a selection is madewhich results in the lowest estimated error, or the predicted highestsimulation quality, being produced. If a selection is made to the effectthat the source element i is to be subdivided, i is subdivided intosource elements at step 905. Subdivision of a cluster results in theidentification of component cluster elements, and/or component objectelements. If, however, the element that is being subdivided is anobject, the subdivision process at step 905 may create new elements.Typically, when a mesh is being created, this will result in the elementbeing split up into four new elements. At subsequent levels ofrecursions, these mesh elements may themselves be further split, intousually four new elements, and so on, until the desired level ofresolution is achieved in order to attain the required level of quality.

If an assessment is made at step 904 to the effect that the receivingelement j is to be subdivided, control is directed to step 908 and asubdivision of j into receiving elements, in a similar manner, isperformed at step 908.

At step 906, the processes of the flowchart shown in FIG. 9, and ofwhich step 906 is a part, are repeated, by considering each of the newlyidentified element subdivisions as a source element. This step is arecursive step, and when this step is performed, at the next level ofrecursion, it may be understood that each of the newly identified sourceelements is then considered in its turn as element i, as determined atstep 901. On exiting the recursive step at step 906, control is directedto step 907, where a question is asked as to whether any additionalnewly identified elements remain to be considered as emitters. Ifanswered in the affirmative, control is directed back to step 906, wherethe next newly identified element is considered. Alternatively, all newelements have been considered. This represents the exit condition forthe whole of the flowchart of FIG. 9.

Similar processes are performed at steps 908, 909 and 910, where newlyidentified elements are considered as receiving elements. In therecursive step 909 each newly identified receiving element is consideredas receiving element j at step 901 in the next level of recursion.

Subdivisions continue to be created recursively until the question askedat step 903 is answered in the negative. At this point, a specificelement has been defined as an appropriate source element and anappropriate element has been defined as a suitable receiving element. Atstep 911 a link is created between these elements which establishes thata transfer of light is considered as being effected between theseelements for the purpose of radiosity calculations. Thereafter, at step912, a form factor Fij is calculated representing the interaction interms of light being transferred from the source element i to thereceiving element j.

After the execution of step 912 it is likely for the procedure to bewithin a recursive operation. Under these circumstances, emerging fromstep 912 is equivalent to emerging from step 906 or step 909.

Eventually, all of the elements will have been considered from theclusters at the highest level down to the smallest newly created meshelements. This results in links and form factors being generated acrossa variety of levels, for example between large clusters and smallelements, between clusters, and between small mesh elements. In total,this complex network of relationships defines light interactions betweenall surfaces in the scene, but at levels of resolution appropriate tothe level of quality that is required. Thus, less links are created whena chair cluster interacts with a distant wall cluster, than if thecomponent objects of these clusters were to be considered, in all theircombinations, as an appropriate description for light energy transfer.These links, therefore, are established between appropriate levels inthe hierarchy of elements, such that interactions are only consideredwhich result in equal to or just above the required level of imagequality.

Operations performed in accordance with the recursive proceduresillustrated in FIG. 9 result in a linked structure being developed ofthe type represented in FIG 10. Objects at a first level representing anobject within the scene shown in FIG. 4 may be recursively subdividedinto constituent elements until a level is reached at which the smallestrequired mesh elements are established. Objects include the statue base410, the statue 404, the first wall 401, the second wall 402, the floor403 and the picture 405. Within the data structure, these objects areclustered so that the base 410 and the statue 404 may be considered as astatue with base cluster 1001. Similarly, the first wall 401, the secondwall 402, the floor 403 and the picture 405 are considered as a roomcluster 1002. The statue with base cluster 1001 and the room cluster1002 are then unified into a scene cluster 1003, which also includes thelight source 406.

In the illustration shown in FIG. 10, straight lines, such as 1005connecting the scene 1003 with room 1002, represent a geometricrelationship between elements. Radiosity links, generated in step 911 inFIG. 9, are illustrated by curved arrowed lines, such as line 1007illustrating an interaction between the statue and base cluster 1001with the second wall object 402. This interaction is expressed by a formfactor associated with the link that represents the amount of lighttransferred from the statue with base cluster 1001 to the wall 402.

The data structure illustrated in FIG. 10 does not attempt to becomplete, and only shows a small fraction of the structure that would becreated in order to fully represent the interactions in a typical scenesuch as the one shown in FIG. 4.

As an example, the recursive refinement procedure detailed in FIG. 9,will endeavour to define an interaction between the first wall 401 andthe second wall 402. On this occasion, a calculated error value given atstep 902 is too high for form factors to be used in terms of wall 401transferring light to wall 402 and in terms of wall 402 reflecting lightback to wall 401. Consequently, in order for the required level ofquality to be achieved, it is necessary for these walls to berecursively divided into smaller elements and for the interactions to bedefined in terms of appropriate element levels in preference to theinteraction directly between the wall objects. The wall 401 has beensubdivided into four mesh elements 1012, 1013, 1014 and 1015. Similarly,wall object 402 has been subdivided into mesh elements 1017, 1018, 1019and 1020.

Link 1022 shows that it is possible to calculate a valid form factorwith element 1014 being a source element and element 1020 being areceiving element. Similarly, link 1023 shows that it is possible tocalculate a valid form factor with element 1014 as a source element andelement 1019 as a receiving element. However, the required level ofquality cannot be achieved if form factors are established for element1012 as a source element and element 1020 as a receiving element. Inorder to generate appropriate calculations with respect to this portionof the scene, it is necessary to further recursively subdivide theseelements.

Thus, when considered as a source element, element 1012 is subdividedinto four elements 1025, 1026, 1027 and 1028. Similarly, as a receivingelement, element 1020 is further subdivided into elements 1031, 1032,1033 and 1034. However, further recursion has indicated that element1025 requires further subdivision, resulting in the generation of meshelements 1036, 1037, 1038 and 1039. At this level, it is now possible tomake progress and it has been established that a form factor can becalculated with element 1039 as a source element and element 1031 as areceiving element illustrated by link 1041. Similarly, link 1042 showsthat element 1039 may be a source element and element 1032 may be areceiving element. Further recursion on the receiving side is notrequired and element 1020 is fully satisfied as a receiving element inrelation to element 1039 by links 1043 and 1044 connecting to elements1033 and 1034 respectively.

The relationship with mesh element 1039 and elements 1031 to 1034 showsthat the recursive refinement steps of FIG. 9 have been performed to asufficient depth in order to provide the level of quality required.

FIG. 10 presents a graphical illustration of the type of data structurethat is used for the multi-resolution representation of the radiosityequation. It will be understood that a true representation for a typicalscene containing many thousands of objects would be impossible topresent in the form of an illustration, and FIG. 10 is intended purelyas an indication of data structures that are being used.

Procedure 702 for the solving of the radiosity equation is detailed inFIG. 11. Each element and object in the scene has an illumination value,and it is the purpose of the radiosity equation to determine anillumination value Bi for all n elements within the scene. Theillumination values will be made up from self emissions from theelements or objects themselves, which will be zero except for lightsources, in combination with contributions from other elements to whichlinks have been constructed of the form indicated in FIG. 10.

At step 1101 all illumination values for all of the elements Bn areinitialised to be equal to their self emission values En which, with theexception of the light sources, will be zero.

At step 1102 illumination contributions for the scene are gathered. Foreach element, incoming contributions, defined by incoming links, aresummed to provide an initial illumination value. These illuminationvalues are not complete in that incoming links occur at differentlevels. Thus, referring to FIG. 10, element 402 receives a contributionfrom element 1001 via link 1007. In addition, its sub-elements 1017 to1020 also receive contributions from element 1014 etc such that, thegathering process identified at step 1102 will result in values beingaccumulated at element 402 and for example, values being gathered atelement 1020. However, in reality, element 1020 represents a portion ofelement 402 and the illumination of element 402 should be equal to thearea average of the illumination values of its sub-elements 1017 to1020.

In order to determine accurate values for the elements, taking accountof contributions made at different mesh elements levels, a push-pullradiosity procedure is performed at step 1104. In order to initiate thisprocedure a variable Bdown is set to zero at step 1103.

After completing the push-pull radiosity operation for the first time,processes 1102, 1103 and 1104 are repeated, such that a first iterationmay be compared against a second iteration to determine the extent towhich estimated illumination values are converging to a stable solution.If the difference between results of these iterations is stillconsidered to be too large, thereby indicating that convergence has nottaken place, the question to this effect is answered in the negative atstep 1105, and a further iteration of steps 1102 to 1104 is repeated.The question at step 1105 is asked again and ultimately sufficientconvergence should take place such that the question asked at step 1105is answered in the affirmative. Typically eight to twelve repetitions ofthese steps will be required in order to reach a suitably stable set ofillumination values.

A known method for step 1102, gathering radiosity for the scene, shownin FIG. 11, is detailed in FIG. 12. At step 1201 a current element isidentified as a receiver j and at step 1202 the illumination of j isinitialised to zero.

A loop is initiated at step 1203 where the next link to a sourceelement, identified as element i, is selected. At step 1204 theillumination across the link from element i to element j is accumulatedand at step 1205 the question is asked to whether element j has any morechild or sub-elements to be considered. If this question is answered inthe affirmative, the whole procedure 1102 is recursively called at step1206. This repeats until all of the sub-elements have been considered,whereafter at step 1207 a question is asked as to whether any remaininglinks to the current receiving element are present. When answered in theaffirmative, control is returned to step 1203 and the next link to thereceiving element j is selected.

A known procedure for step 1103, the push-pull process for theillumination in the scene, shown in FIG. 11 is detailed in FIG. 13. Atstep 1301 the current element is considered as p and on the first loopthe current element will be that of the highest level of the structureshown in FIG. 10 which, in this example, would be the whole scenerepresented by cluster 1003. At step 1302 a question is asked as towhether p, selected at step 1301, has child elements and when answeredin the affirmative control is directed to step 1304. At step 1304 avariable Bup is set equal to zero, whereafter at step 1305 a next childq of selected element p is selected.

Thereafter, the whole of the procedure shown in FIG. 3 is recursivelyexecuted at step 1306. Within the execution of the recursive step, alocal value for Bdown is set equal to the current value for Bdown plusBp, that is the illumination gathered directly at the parent element p.The result, in terms of a local value for Bup is stored in variableBtemp. Thereafter, control is directed to step 1307.

At step 1307 variable Bup is set equal to value Btemp, the local valuedetermined by the recursive call to procedure 1306 which is thenmultiplied by the area of the child divided by the area of the parent tocompute an area average.

At step 1308 a question is asked as to whether another child of p ispresent and, when answered in the affirmative, control is directed backto step 1305. When all of the children have been considered, thequestion asked at step 1308 will be answered in the negative and controlis directed to step 1309, resulting in a new value for Bp being setequal to Bup. When the question asked at step 1302 is answered in thenegative, to the effect that the current element p does not have anychildren, Bup is set equal to Ep, the self emission value for element p,plus Bp plus Bdown, and control is directed to step 1309.

In an alternative embodiment, the steps shown in FIG. 7 are performediteratively, as part of a loop. The purpose of this is to facilitate amore accurate determination of error values, upon which decisions aremade about the level of meshing that is to be performed. In theiterative process, during the first pass of the steps shown in FIG. 7,at step 701, the multi-resolution representation is constructed for afirst error tolerance, eps_(—)1, and then at step 702, the radiosityequation is solved to yield a first solution. On the next iteration, theerror tolerance is reduced, to eps_(—)2. However, the multi-resolutionrepresentation constructed at step 701 in the previous iteration isalready valid down to the eps_(—)1 level of error tolerance. Thus, tocontinue to the reduced level of error tolerance, given as eps_(—)2, thepre-existing multi-resolution representation can be continued by furtheraddition of mesh elements and establishing links and there is no wastagein having to recalculate existing data structures. A third andadditional iterations may then be performed.

A first purpose of this multi-pass method is to enable a rough displayof the radiosity solution to be previewed more quickly than if the fullydetailed solution is created in one stage. It is possible, then, for anoperator to identify obvious deficiencies at an early stage. A furtheradvantage is that the first, or early solutions, provide subsequentsolutions with information about the magnitude of light transferredacross links, and not just the magnitude of the form factor. Thisinformation can be used to improve the accuracy by which errors arepredicted, such that even pairs of surfaces with large form factors donot need to be respectively meshed, if the actual light that would betransferred across those links is insignificant. This form of iterativerefinement is known as BF refinement.

The hierarchical sub-division as illustrated at 607, is directed towardsdividing regions into very small elements, where maximum benefit isderived from this division, while in other areas retaining relativelylarge elements so as to reduce computation demands. Problems with thisapproach arise if surfaces intersect along boundaries that are notaligned with mesh element boundaries. This situation is illustrated inFIG. 14.

In FIG. 14 there are three walls. A vertical wall, 1401 forms a rightangle with a floor surface 1403, and a dividing wall surface 1402. Eachof the surfaces 1401, 1402 and 1403 has been sub-divided into meshelements. However, the full level of meshing required has not beenshown, in order to preserve clarity for the purposes of the presentdescription. The floor 1403 has been sub-divided into a plurality ofmesh elements 1411 to 1414. The base of the dividing wall 1402intersects the floor 1403 along a boundary that is not aligned with theborders of mesh elements 1411 or 1412. If the multi-resolutionsimulation of the radiosity equation is constructed with mesh elementsthat are crossed by other surfaces (either touching or intersectingthese elements), such as dividing wall 1402, a problem occurs with lightleaks.

Mesh elements 1413 and 1414 receive light from the environment boundedby the dividing wall 1402, the floor 1403 and the rear wall 1401, to theright of the dividing wall 1402. However, as each mesh element isconsidered as having a uniform brightness, the lighting of the portionof the mesh element 1411 that is to the left of the dividing wall 1402will be inappropriate to the volume in which it is located. A similarproblem occurs with the left portion of the mesh element 1412.Furthermore, light interactions occurring to the left of the dividingwall 1402 will contribute to the brightness of mesh elements 1411 and1412 in a way that is inappropriate to the brightness of these elementswithin the environment to the right of the dividing wall 1402. Theseproblems may be generally considered as light leaks.

The same problems occur at the intersection of the rear wall 1401 withdividing wall 1402. These problems occur wherever surfaces touch orintersect, unless their line of contact coincides with mesh elementboundaries. Such coincidence is likely to occur where, for example, theedges of walls meet, such as at the intersection of the floor 1403 withthe rear wall 1401. However, in many instances within a typical scene,intersections are not clearly defined as occurring at boundaries thatwill coincide with mesh element boundaries, and light leaks will occur.

A solution has been proposed for the problem illustrated in FIG. 14.This is described in “Making Radiosity Usable” by Daniel R. Baum,Stephen Mann, Kevin P. Smith, James M. Winget, in ACM SIGGRAPH ComputerGraphics, Vol. 25, No. 4 (July 1991), Pages 51-60. This referencediscloses that it is possible to resolve the problems of light leaks bysub-dividing surfaces into mesh elements along surface intersections.

FIG. 15 details the result of performing mesh sub-division of thesurfaces shown in FIG. 14, in accordance with identified surfaceintersections. The floor 1403 has been divided into two separatelymeshed areas, comprising a first area to the left of the dividing wall1402, comprising mesh elements 1501 to 1504, and a second area of thefloor 1403, to the right of the dividing wall 1402 that is sub-dividedinto differently sized mesh elements 1505 to 1508. The rear wall 1401 issimilarly meshed in accordance with the intersection of the dividingwall 1402. This arrangement results in zero light leaks of the type thatwere a problem with the arrangement shown in FIG. 14.

Although it is known to implement a solution of the type shown in FIG.15, known techniques for subdividing the mesh elements during theradiosity simulation so that their boundaries match lines of contact orintersection between pairs of surfaces in the original scene, are veryinefficient.

An improved method for step 701, of constructing a multi-resolutionsimulation of the radiosity equation, is shown in FIG. 16. At step 1600a check is made for intersecting polygons. Within this step,intersecting polygons are identified, and the original surfaces are thensplit along lines of intersection wherever these occur. The resultingsurfaces are used as a modified scene description for the radiositysimulation. Subsequently steps 801, 802 and 803, shown in FIG. 16operate substantially as described with reference to FIG. 8.

The check for intersecting surfaces (or polygons), performed at step1600 in FIG. 16 is detailed in FIG. 17. At step 1701 a hierarchy ofbounding volumes is constructed. It is possible, in an alternativeembodiment, that a hierarchy of bounding volumes already exists for thepurpose of clustering for a faster radiosity simulation or for use as anacceleration scheme in visibility computations that are also used duringthe radiosity computations. At step 1702 the whole scene volume isselected as a starting pair of items. Thus, a pair of items isidentified, each of which is the whole scene volume. At step 1703 acheck is made for intersecting polygons using a search within thehierarchy of bounding volumes identified at step 1701. At step 1704surfaces of intersecting polygons identified at step 1703 are splitalong their lines of intersection, so that the resulting surfaces arethen used as part of a modified scene description that is used forconstructing the radiosity simulation.

The hierarchy of bounding volumes generated at step 1701 is illustratedby way of a two-dimensional example shown in FIG. 18. Algorithms forconstructing a hierarchy of bounding volumes are known. One suchalgorithm is described by Jeffrey Goldsmith and John Salmon in“Automatic Creation of Object Hierarchies for Ray Tracing”, IEEEComputer Graphics & Applications, May 1987, pages 14-20. In constructingthe hierarchy of bounding volumes, surfaces are grouped into boundingvolumes according to proximity and smaller bounding volumes are groupedinto larger bounding volumes to form the hierarchy. The resultingbounding volumes may overlap.

Having created the hierarchy of bounding volumes, it becomes possible toidentify very quickly, which bounding volumes do not touch or overlap,and therefore exclude polygons contained within separate boundingvolumes from the possibility of intersection. In the example shown inFIG. 18, all scene polygons are bounded by a largest bounding volume1811. This volume contains a hierarchy of smaller bounding volumes 1811to 1819, some of which may overlap each other, as is the case withbounding volumes 1812 and 1813. Any bounding volume may containpolygons, such as polygon 1821, or other bounding volumes, such asbounding volumes 1831 and 1832. Pairs of polygons within the samebounding volume may overlap, as is shown with polygons 1822 and 1823 inbounding volume 1816. However, polygons in non-overlapping boundingvolumes, such as polygons 1822 and 1821 are automatically excluded fromthe need to check whether they are overlapping by the fact that boundingvolumes 1812 and 1816 do not overlap.

Within the volume 1812 is a further volume sub-division 1833, thatcontains polygons 1826 and 1827. Clearly any polygons that are notcontained in the bounding volume 1833 cannot intersect any polygonsinside it. Thus, polygon 1821 cannot intersect either polygon 1826 orpolygon 1827. Because there are no further sub-divisions of volume 1833,it then becomes appropriate to check for intersection between thepolygons contained in its volume, in this case polygon 1826 and polygon1827. In this case, the polygons are shown as intersecting, and it willbe necessary to store this information such that appropriate surfacesub-divisions can be made at step 1704.

Polygon 1824 is contained in bounding volume 1812, and polygon 1825 iscontained in bounding volume 1813. Although both these bounding volumes1812 and 1813 overlap, neither of them contains both polygons 1824 and1825. Nevertheless, as shown in the illustration, it is possible thatthese polygons do intersect. The invention takes account of thispossibility, and will identify the polygons 1824 and 1825 asintersecting.

A systematic algorithm for checking intersecting polygons in accordancewith these rules is detailed in FIG. 19. At step 1901 the initial pairof items is identified as A and B. Thus, in the initial conditions, thewhole scene volume will be considered as being A and also B. At step1902 a question is asked as to whether A and B are both polygons. Ifanswered in the negative, control is directed to step 1904. At step 1904a question is asked as to whether A and B overlap. In the initial casewhere A and B are both the whole scene volume, the answer to thisquestion is yes. Thereafter control is directed to step 1905. At step1905 a comparison is made of the volumes of A and B. If A is greaterthan B, control is directed to step 1906. Alternatively, if B is greateror equal to A, control is directed to step 1909. This will be the caseon the initial condition when A and B are both selected as being thewhole scene volume. At step 1906 an identification is made of the nextchild of A. Thus, when the whole scene volume 1811 is being considered,a child of A could be any of bounding volumes 1812 to 1819.

At step 1907 the flow chart of FIG. 19 is called for items X and B.Thus, in the next instantiation of the process represented by thisflowchart, X and B become identified at step 1901 as items A and B. Atstep 1908 a question is asked as to whether there is another child of A.If answered in the affirmative, control is directed back step 1906.Alternatively, if there are no child volumes of A, control is directedout of the flow chart shown in FIG. 19.

If the result of comparing volumes at step 1905 is that the volume of Bis considered as being greater than or equal to A, control is directedto step 1909. At step 1909 an identification is made of the next childof B as being identified as X. Thus, any of volumes 1812 to 1819, may beidentified as X at step 1909. At step 1910, the flow chart of FIG. 19 iscalled for items A and X, with A and X being identified as items A and Bon each instantiation of the process represented by the flowchart. Atstep 1911 a question is asked as to whether there is another child of Bavailable for consideration. If answered in the affirmative, control isdirected to step 1909, where additional bounding volumes may beconsidered. Alternatively, if the question asked at step 1911 isanswered in the negative, the processes for FIG. 19 are completed.

Completion of these processes may result in a return to a higher levelof operation of the flowchart shown in FIG. 19. If the question asked atstep 1902 is answered in the positive, and A and B are both polygons,control is directed to step 1903. At step 1903 a check is made forintersection of A with B. If A and B do intersect, a sub-division tableis updated.

The amount of time taken to recursively check for intersecting polygonsusing the method detailed in FIG. 19, and which is indicated at step1703 in FIG. 17, is proportional to the number of polygons in the scene.This may also be represented as being a problem having O(n) complexity.Construction of the hierarchy of bounding volumes, illustrated in FIG.18, and shown at step 1701 in FIG. 17 has a greater complexity ofO(n.log(n)). This is still less than the problem of identifying thepossible intersection of every possible pair of polygons, which is aproblem of O(n²) complexity. However, as previously stated, thehierarchy of bounding volumes may already have been created for otherpurposes.

Checking for the intersection of polygons requires that many floatingpoint multiplications be performed. The invention avoids unnecessarilyrepeating such complex mathematical processes by considering therelationships between bounding volumes containing polygons, rather thanthe polygons themselves. The sides of the bounding volumes are alignedwith the x, y and z axes of the global co-ordinate system. Thus, whenconsidering whether or not bounding volumes overlap, only additions orsubtractions are required.

Within the process disclosed in FIG. 19, a condition is eventuallyreached when both items A and B are polygons themselves, at which pointit becomes necessary to perform the sequence of mathematical operationsthat is necessary to determine whether the polygons intersect. However,because this operation needs to be performed so rarely, in comparison tothe square of the number of polygons within the scene, the time taken todetermine which polygons in the scene are intersecting, is greatlyreduced.

The information stored at step 1903, is eventually used when performingstep 1704 shown in FIG. 17. In this way, polygons that intersect aredivided along their lines of intersection prior to the steps ofradiosity simulation, so that the mesh elements created from thesepolygons will have edges that align with the lines of intersection.

The artificial scene shown in FIG. 4 may be combined with images from areal studio, such that artificial objects, walls and studio features maybe superimposed upon a real studio in which minimal features arepresent. The combination of real and artificial images in this wayresults in the creation of a virtual set, in which real and virtualobjects may be mixed. An example of a virtual set is shown in FIG. 20. Acamera 2001 generates live video image data, as well as serialpositioning data and lens data. The camera is aimed at talent 2002,located in the centre of a blue screen environment, comprising a bluescreen floor 2003 and walls 2004. The blue colour of the walls iscarefully controlled and calibrated in such a way as to facilitateautomatic replacement of any blue areas of the subsequently processedcamera images with a corresponding virtual image. A monitor 2005facilitates visual feedback for the talent, such that it is possible tointeract in a more natural way with objects in the virtual world.

Equipment for compositing image data from the virtual set shown in FIG.20 with artificial scene images such as the one shown in FIG. 4, isdetailed in FIG. 21. A main processor 2101, such as an Onyx2™,manufactured by Silicon Graphics Inc, receives image and position datasignals from the camera 2001 shown in FIG. 20. The position informationfrom the camera, together with lens data, including zoom and focus,enable a calculation to be made of the viewpoint of the camera withrespect to the virtual set. The walls of the virtual set are calibratedin position, so that at least one of either the floor or the two wallsmay be used as a reference plane that will match with a correspondingfloor or wall plane in the artificial scene shown in FIG. 4. Commandsfor controlling the virtual environment are performed by the operatorusing a mouse 2105, a keyboard 2104 and a monitor 2102. A high qualitybroadcast monitor 2103 is also provided on which to view the results ofthe compositing process.

The operator has control over such parameters as blue screen removal,floor plane or wall plane tolerance mapping, quality control, ensuringthat calibrations are maintained and so on. The main processor 2101renders the scene shown in FIG. 4 in accordance with the radiositysimulation process described previously. Once this step has beenperformed, it then becomes possible to render the scene from anyviewpoint. In a virtual set, the viewpoint is defined by the cameraposition and lens conditions. Thus, the main processor 2101 performsradiosity rendering in response to signals from the camera 2001. Therendered scene is then keyed with the real video data using a bluescreen keyer process, such that the talent 2002 appears to be in ahighly realistic scene, comprising the objects shown in FIG. 4. As isknown, additional lighting effects may be added, in order to supportview dependent lighting.

What we claim is:
 1. A method of generating image data for a scenecomprising: identifying a line of intersection of contact between two ormore objects displayed in a three dimensional scene by analyzingsurfaces of said objects using a hierarchy of bounding volumes, whereina bounding volume contains one or more of the objects; dividing one ormore polygons along the line of intersection or contact; subsequent todividing the one or more polygons along the line of intersection,constructing a multi-resolution representation of the radiosity equationfor said scene, wherein one of said identified surfaces is consideredseparately for light emission on one side of a line of contact orintersection and then considered for light emission on a reverse side ofsaid line of contact or intersection; and generating and displaying saidscene based on the radiosity equation.
 2. A method according to claim 1,wherein said step of identifying a line of intersection or contact byanalysis of bounding volumes, comprises the component steps of:considering bounding volumes and surfaces is items; identifying pairs ofitems; determining whether both items in the pair are surfaces;determining an overlap of items or an intersection of surfaces; and uponcondition of an overlap, recursing the above component seeps, retainingthe smaller item and selecting another; or upon condition of anintersection, storing indication of this condition.
 3. A methodaccording to claim 1, wherein said hierarchy of bounding volumes iscreated for the dual purpose of identifying intersecting or touchingsurfaces, and an additional method for generating image data from saidscene.
 4. A method according to claim 1, wherein when dividing, meshelements created from the one or more polygons have edges that alignwith the line of contact or intersection.
 5. An apparatus for generatingimage data from scene data comprising: means for identifying a line ofintersection or contact between two or more objects displayed in a threedimensional scene by analyzing surfaces of said objects using ahierarchy of bounding volumes, wherein a bounding volume contains one ormore of the objects; means for dividing one or more polygons thatintersect along the line of intersection or contact; means forconstructing, subsequent to the dividing, a multi-resolutionrepresentation of the radiosity equation for said scene, wherein one ofsaid identified surfaces is considered for light emission on one side ofa line of contact or intersection and then considered for light emissionon a reverse side of said line of contact or intersection; and means fordisplaying said scene.
 6. Apparatus according to claim 5, wherein themeans for identifying a line of intersection or contact by analysis ofbounding volumes comprises: means for considering bounding volumes andsurfaces as items; means for identifying pairs of items; means fordetermining whether both items in said pair are surfaces; means fordetermining an overlap of items or an intersection of surfaces; andmeans for upon condition of an overlap, recursing the above componentsteps, retaining the smaller item and selecting another; or means forupon condition of an intersection, storing an indication of thiscondition.
 7. Apparatus according to claim 5, further arranged such thatsaid hierarchy of bounding volumes may be created for the dual purposeof identifying intersecting or touching surfaces, and an additionalmethod for generating image data from said scene.
 8. Apparatus accordingto claim 5, wherein when dividing, mesh elements created from the one ormore polygons have edges that align with the line of contact orintersection.
 9. A computer-readable medium having computer-readableinstructions executable by a computer such that said computer performssteps for generating image data for a scene, comprising the steps of:identifying a line of intersection or contact between two or moreobjects displayed in a three dimensional scene by analyzing surfaces ofsaid objects using a hierarchy of bounding volumes, wherein a boundingvolume contains one or more of the objects; dividing one or morepolygons that intersect along the line of intersection or contact;subsequent to dividing the one or more polygons along the line ofintersection, constructing a multi-resolution representation of theradiosity equation for said scene, wherein one of said identifiedsurfaces is considered separately for light emission on one side of aline of contact or intersection and then considered for light emissionon a reverse side of said line of contact or intersection; andgenerating and displaying said scene based on the radiosity equation.10. A computer-readable medium according claim 9, wherein saidinstructions are executed by said computer, such that said step ofindentifying a line of intersection or contact by analysis of boundingvolumes comprises the component steps of: considering bounding volumesand surfaces as items; identifying parts of items; determining whetherboth items in a pair are surfaces; determining an overlap of items or anintersection of surfaces; and upon condition of a overlap, recursing theabove component steps, retaining the smaller item and selecting another;or upon condition of an intersection, storing an indication of thiscondition.
 11. A computer-readable medium according to claim 9, whereinsaid instructions are executed by said computer, such that saidhierarchy of bounding volumes is created for the dual purpose ofidentifying intersecting or touching surfaces, and an additional methodfor generating image data from said scene.
 12. A computer-readablemedium according to claim 9, wherein said instructions are executed bysaid computer such that when dividing, mesh elements created from theone or more polygons have edges that align with the line of contact orintersection.
 13. The method of claim 1 wherein when identifying a lineof intersection or contact, objects from non-overlapping boundingvolumes are automatically excluded as not intersecting or touching. 14.The apparatus of claim 5 wherein when identifying a line of intersectionor contact, object from non-overlapping bounding volumes areautomatically excluded as not intersecting or touching.
 15. The computerreadable medium of claim 9 wherein when identifying a line ofintersection or contact, objects from non-overlapping bounding volumesare automatically excluded as not intersecting or touching.